Contrasting Ultra-Low Frequency Raman and Infrared Modes in Emerging Metal Halides for Photovoltaics

Lattice dynamics are critical to photovoltaic material performance, governing dynamic disorder, hot-carrier cooling, charge-carrier recombination, and transport. Soft metal-halide perovskites exhibit particularly intriguing dynamics, with Raman spectra exhibiting an unusually broad low-frequency response whose origin is still much debated. Here, we utilize ultra-low frequency Raman and infrared terahertz time-domain spectroscopies to provide a systematic examination of the vibrational response for a wide range of metal-halide semiconductors: FAPbI3, MAPbIxBr3–x, CsPbBr3, PbI2, Cs2AgBiBr6, Cu2AgBiI6, and AgI. We rule out extrinsic defects, octahedral tilting, cation lone pairs, and “liquid-like” Boson peaks as causes of the debated central Raman peak. Instead, we propose that the central Raman response results from an interplay of the significant broadening of Raman-active, low-energy phonon modes that are strongly amplified by a population component from Bose–Einstein statistics toward low frequency. These findings elucidate the complexities of light interactions with low-energy lattice vibrations in soft metal-halide semiconductors emerging for photovoltaic applications.

and was subtracted from the measured Raman spectra recorded in the presence of a sample.
All Raman spectra were intensity corrected using a tungsten-filament reference lamp of known emissivity spectrum.Also, the intensity of Raman scattering is directly proportional to the fourth power of the frequency, which has been corrected for all Raman spectra. 2 The band pass and notch filters have FWHM linewidth of 5cm -1 .Therefore, we regard the lower limit of the accessible range as ~7cm -1 , but this can vary from sample to sample depending on the exact alignment for each sample, sample surface quality etc.
Figure S1 Normalised Raman intensity spectra of a z-cut quartz, the substrate used throughout this study.A CW laser with wavelength 900nm was used as the light source, and the Raman signal was collected in a back-scattering geometry.Rayleigh scatter was suppressed with volume-Bragg notch filters.Experimental details can be found in Supporting Information Section 1.1 above.

Terahertz time-domain spectroscopy (THz-TDS)
4][5] Briefly, an amplified Ti:Sapphire laser system was used for generation and detection of THz pulses, with characteristics ~ 35 fs pulse duration, 800 nm central wavelength, 5 kHz repetition rate (MaiTai -Ascend -Spitfire regenerative amplifier from Newport Spectra Physics).THz pulses were generated using a tri-layer spintronic emitter (2 nm tungsten, 1.8 nm Co40Fe40B20, 2 nm platinum on a quartz substrate).These were focused onto the thin films deposited on z-cut quartz substrates using gold-coated off-axis parabolic mirrors, and then onto a 1 mm-thick (110)-ZnTe crystal for electro-optic sampling.The polarisation of the gate beam was detected with the combination of a quarter-wave plate, polarising beam splitter and a balanced photodiode.A home-made field-programmable gatearray-based board was used for data acquisition.Relative time delays were controlled using optical delay stages.We take ~0.5THz as the lower limit of our detection due to the lower frequency components not being able to be fully collected by OAPs and also not being focused tightly onto the detection crystal.

MAPbI3 single crystals
The MAPbI3 perovskite single crystals were prepared via inverse temperature crystallization. 8,9pically, 1.3 M CH 3 NH 3 PbI 3 precursors were prepared by adding 2.3 g lead iodide (PbI 2 ) and 0.8 g methylammonium iodide (MAI) into 3.85 mL -butyrolactone (GBL), heated at 90 o C for 2 hours with stirring.Then, the precursor solutions were filtered with syringe filters (0.22 m pore size) and transferred to clean containers, which were kept on a stable hot-plate and heated at 130 o C for 3 hours.Crystals were formed on the bottom of the containers.Finally, the crystals were collected and dried at 60 o C in glovebox for 2 hours.

FAPbI3 thin films
FAI and PbI2 were co-evaporated with the molar ratio of FAI:PbI2= 1:1 on the z-cut quartz substrate in a custom-built thermal evaporator chamber.During the evaporation, the pressure was typically < 5 × 10 -6 mbar.The sublimation rate of the precursors was controlled using goldplated quartz microbalances adjacent to the crucible and a PID-loop-control software.Unless specified otherwise, all samples were annealed in an N2 glovebox at 150 °C for 5 minutes and at 135 °C for 25 minutes.After cooling down to room temperature, films were ready to use.

CsPbBr3 thin films
A Bridgman-grown single crystal of CsPbBr3 was gently ground into a fine powder in a nitrogen-filled glove box.The starting material was placed in a thermal evaporator crucible.
Quartz substrates were ultrasonically cleaned in Hellmanex® III (2% in water), deionized water, acetone, and isopropanol for 15 min at each stage, followed by UV ozone treatment for 10 min.The thickness of the fabricated films was controllable by the mass of the deposition material (200 mg of starting material to obtain 100 nm perovskite film).The vacuum of the evaporation chamber was reduced to 10 −6 Torr.The substrate temperature was typically 20 °C.
The deposition temperature was in the range 400-500 °C.The deposition rate was 0.6 Å/s.The substrate rotation velocity was 10 rpm.After the evaporation, the films were aged at room temperature in a nitrogen-filled glove box for one month.
2.5 CsPbBr3 single crystals 2.5.1 Synthesis and Purification Runs: 6.423 g of CsBr (ChemCraft, 99.999%) and 11.077 g of PbBr2 (Sigma Aldrich, 99.999%) were mixed and ground together thoroughly using a mortar in an Ar glovebox.This material was then flame-sealed under 1.4 x 10 -2 mbar vacuum into a fused silica ampule (i.d. 10 mm) with a sharp tip.This ampule was placed in the hot zone of a custom-built 3-zone Bridgman furnace (HTM Reetz), and the temperatures were set to 675 o C, 400 o C, and 400 o C. The sample was left overnight to ensure a full melt and synthesis reaction, then moved through the furnace at a speed of 0.081 mm/min (4.86 mm/hr) while undergoing 0.3 rpm rotation until it had passed outside the furnace.The resulting ingot had some black impurities near the top, so the sample was reset and the same temperature profile applied, and moved through the furnace more slowly (0.042 mm/min, 2.52 mm/hr) to fully segregate these impurities.The resulting ingot was opened in the Ar glovebox and the black regions at the top of the ingot (typically carboncontaining impurities from PbBr2 precursor) were cut off and discarded, and the material was broken into chunks (to reduce the risk of thermal expansion cracking the ampule) and flamesealed under 1.1 x 10 -2 mbar vacuum into a new fused silica ampoule (i.d. 10 mm) with a sharp tip.This process removes the impurities for higher-quality growth.A final purification run, with identical conditions to the previous run (0.042 mm/min, 0.3 rpm, temperatures of 675 o C -400 o C -400 o C) showed no further black impurities present, confirming that the material was sufficiently pure to yield higher crystallinity.

Bridgman Crystal Growth:
The Vertical Bridgman method was used to grow the large single crystals of CsPbBr3.The ampoule was reset to the hot zone for the Bridgman Growth.The zone 1 temperature was set to 650 o C with a 150 o C/hr ramp rate, and held for 12 hours to ensure a full melt before sample motion occurred.The zone 2 and 3 temperatures were set to 375 o C.These temperatures were held for 350 hours while the ampule was moved through the furnace at a rate of 0.015 mm/min (0.9 mm/hr) under 0.3 rpm rotation.After the motion had ceased, the zone 1 temperature ramped to 375 ºC to make the temperature profile in the furnace uniform.The

Crystal Processing:
The ingot was opened in an Ar glovebox and cut into 2 mm-thick wafers using a Crystal Systems Corporation Cu-02 Desktop Crystal Cutter with Goniometer operating at 60 rpm with oil-based lubricant.The surfaces of these wafers were polished using a Crystal Systems Corporation TP-02 Polisher operating at 20 rpm, with MicroMesh SiC cutting papers used to get successively finer surfaces with a final polish of 12000 grit producing an optical mirror-like surface.These processing steps were completed under Ar to preserve the pristine surfaces and the crystals were sealed under Ar for transport, ensuring that both the raw material and as-grown crystals were never exposed to ambient conditions.

PbI2 thin films
PbI2 was evaporated with the deposition rate of 0.2Å/s on the z-cut quartz substrate in a custom-built thermal evaporator chamber.During the evaporation, the pressure was typically < 5 × 10 -6 mbar.The source rates were kept constant using gold-plated quartz microbalances and a PID-loop-control software.

Cs2AgBiBr6 thin films
The stock solution was prepared by dissolving CsBr (Alpha Aesar, 99.999 % metals basis), BiBr3 (Alpha Aesar, 99.9 % metals basis) and AgBr (Alpha Aesar, 99.998 % metals basis) in 1 mL DMSO (Sigma Aldrich, anhydrous, ≥99.9%) by vigorous stirring at 130 °C for 60 minutes to obtain a 0.5 M solution.All Steps were performed in a nitrogen-filled glovebox with controlled atmosphere.The substrates were cleaned with a detergent (Hellmanex), followed by washing with acetone and ethanol and dried under an air stream.Afterwards, the substrates were cleaned with oxygen plasma for 5 minutes and immediately transferred into the glovebox.
Prior to the spincoating step, the substrates and the solution were placed on a hotplate (Heidolph with internal temperature sensor) at 60 °C to be preheated.The stock solution was constantly stirred.The thin films were fabricated by spincoating the warm solution dynamically (1000 rpm for 10 s, followed by a second step at 6000 rpm for 35 seconds) onto the preheated substrates (70 µL of the solution were dropped immediately after the substrate started to spin at 1000 rpm).After the spincoating, the thin films were annealed at 275 °C for 5 minutes, and the preheating was set at 60 °C.

Cu2AgBiI6 thin films
Thin films of Cu2AgBiI6 were fabricated by vacuum evaporating (BOC Edwards Auto 306) and co-depositing bismuth(III) iodide (Alpha Aesar Puratronic, 99.999%), silver(I) iodide (Alpha Aesar Premion, 99.999%), and copper(I) iodide (Alpha Aesar Puratronic, 99.998%) precursors from three separate, 2.4 cm 3 alumina crucibles and thermal sources.The crucibles and sources were custom-made by Moorfield Nanotechnology to fit the dimensions of the evaporation chamber.The precursors were heated to the temperature corresponding to the following evaporation rates: CuI, AgI, BiI3 = 0.33 Ås -1 (370°C), 0.18 Ås -1 (475°C), and 0.50 Ås -1 (230°C), respectively.Cu2AgBiI6 films were 250 nm thick ((249 ± 13) nm, as measured by a Veeko Dektak 150 profilometer).The rates were measured using three quartz crystal microbalances (QCM) positioned off centre to each sources' vapour cone and an Inficon SQC-310 deposition controller.Prior to the deposition of Cu2AgBiI6, a tooling factor for each precursor was calculated to correct the divergence between the true rate and the rate measured by the QCM.To do this, 100 nm (as measured on the SQC-310 controller) of each precursor was deposited on 30 x 30 mm glass substrates and the thickness was measured using a profilometer.A new tooling factor was calculated using: X-ray diffraction was used to ensure only the binary precursors and no other crystalline impurities were deposited.All depositions were carried out under vacuum (~ 2 × 10 −6 mbar).
The substrates were protected during the heating and cooling process by a mechanical shutter, and the substrates were rotated during deposition to improve surface coverage.No intentional substrate heating was applied.However, the substrates reached a maximum temperature of approximately 60°C during co-deposition due to heat transfer from the sources.The temperature of the substrates was measured using RS Electronics PRO nonreversible temperature sensitive labels (RS Stock No.:779-9779).

AgI thin films
Thin films of silver iodide were fabricated by depositing (using a BOC Edwards Auto 306 evaporator) silver(I) iodide (Alpha Aesar Premion, 99.999%) precursor from 2.4 cm 3 alumina crucibles and thermal sources.The crucibles and sources were custom-made by Moorfield Nanotechnology to fit the dimensions of the evaporation chamber.The precursor was heated to the temperature corresponding to the desired evaporation rates, with the rates measured using a quartz crystal microbalance positioned off centre to the source's vapour cone and an Inficon SQC-310 deposition controller.All depositions were carried out under vacuum (10 -6 mbar).The substrates were protected during the heating and cooling process by a mechanical shutter, and the substrates were rotated during deposition to improve surface coverage.No intentional substrate heating was applied.All films are 250-300 nm thick and were deposited on z-cut quartz substrates.Films were annealed post deposition in a nitrogen glovebox for 15 minutes at 180°C.The evaporation rate was 0.2 Ås -1 .Films were not annealed post-deposition.1and 2 of the main manuscript), acquired with THz-TDS.

Fitting of Raman and THz IR spectra
The text below describes the method employed for fitting Raman and IR THz spectra of metal halides based on a simple damped harmonic oscillator model, with a table (Table 1) listing the extracted mode frequencies and associated broadening provided at the end.
Raman spectra were fitted with the sum of the individual responses expected for a number of damped harmonic oscillators, with the -th individual oscillator response given by: where   , ,   , and Γ i are the amplitude, Bose-Einstein factor, harmonic oscillator frequency, and damping coefficient of -th mode, respectively.
In addition to these damped harmonic modes, a quasi-elastic scattering response was also added 10 as follows: where   and   are the quasi-elastic scattering amplitude and broadening factor, respectively.We note that from fitting we find that the broadening factor for the quasi-elastic scattering is much smaller (<0.25 THz ~ 8cm -1 ) than our interested range for comparison with IR spectra; this quasi-elastic response is a different process to what we are interested in in this study.It has been attributed to rattling of molecular cations in a temperature-dependent Brillouin zone scattering study. 10aphs below show the result of such fits to Raman spectra for a range of metal halide semiconductors, with the extracted parameters given in Table 1 below.In some cases, the frequency range of fitting had to be constrained due to either the presence of very strong substrate Raman peaks, or the Raman response being too broad for any effective fitting.For THz spectra, a similar harmonic oscillator response was used for fits to data, however, the (() + 1) Bose-Einstein term was omitted, given that IR photon absorption and conversion into a phonon does not require prior presence of a phonon population.The response per oscillator mode  is then given by: Graphs below show the result of such fits to THz IR spectra for a range of metal halide semiconductors, with the extracted parameters given in Table 1 below.
We also note that because of the focus on the ultra-low range of frequency (<3 THz) in this study, our measurement window may not necessarily capture all of the optically active modes.Graphs below show the extracted oscillator frequency across the MAPb(BrxI1-x)3 thin-film series, which demonstrate the blueshift of all modes with increasing bromide content x in both Raman and IR responses, as would be intuitively expected for increasing incorporation of the lighter halide.
cooling program was set to slow during the phase transitions occurring near 120 and 90 o C, with a 10 o C/hr cooling rate from 375 o C to 175 o C, a 2.5 o C/hr slow cooling rate from 175 o C to 75ºC, and a 10 o C/hr rate to 30 o C. The resulting CsPbBr 3 ingot was orange-red and had large (5+ mm) transparent single-crystalline domains, though the edges of some portions exhibited twinning.

3
Comparison of Raman spectra for AgI and Cs 2 AgBiBr 6 thin films For clarity, zoomed-in spectra of AgI and Cs2AgBiBr6 are plotted below, focusing on the central region close to the elastically scattered light, in order to demonstrate that the central Raman response is visible for AgI Raman spectra but not for Cs2AgBiBr6.The AgI Raman spectrum clearly exhibits a low-frequency Raman response, whereas Cs2AgBiBr6 Raman spectrum shows a residual Rayleigh scattering, rather than a response from the material.This difference is also apparent in the reduced spectra shown in Figure 3(a) of the main text, where a slow rise in the Raman response is visible from zero frequencies for AgI but not for Cs2AgBiBr6.

Figure S2 .
Figure S2.Normalised Raman intensity spectra of AgI and Cs2AgBiBr6 thin films, focusing on the narrow range close to the central, elastically scattered peak.A CW laser with wavelength 900nm was used as the light source, and the Raman signal was collected in a back-scattering geometry.Rayleigh scatter was suppressed with volume-Bragg notch filters.Experimental details can be found in Supporting Information Section 1 above.

Figure S3 .
Figure S3.Normalised reduced Raman and reduced IR absorption spectra of CsPbBr3, MAPbBr1.5Br1.5,MAPbBr3 and FAPbI3 thin film on z-cut quartz.The reduced Raman spectrum is given by I R /(ω × (n + 1)), where IR is the measured Raman intensity, and the reduced IR spectrum is given by α/ω 2 , where  is the measured THz IR spectrum.A laser wavelength of 900nm was used for non-resonant Raman spectroscopy and THz-TDS was employed for acquisition of the IR absorption spectrum, as detailed in Supporting Information Section 1 above.The equivalent spectra for MAPbI3 thin films are shown in Figure2of the main manuscript.

Figure
Figure S4 (a) Normalised reduced Raman spectra of metal halides deposited as thin films on z-cut quartz.(b) Normalised IR absorption of the same metal halides (equivalent to the reduced Raman spectra, as can be seen from Equation 1 and 2 of the main manuscript), acquired with THz-TDS.

Figure S5 .
Figure S5.Damped harmonic oscillator model fits (solid lines) to the experimentally recorded (solid circles) Raman response of a MAPbI3 thin film.Fits reflect the sum over three phonon modes, together with a small quasi-elastic (QE) scattering response.

Figure S6 .
Figure S6.Damped harmonic oscillator model fits (solid lines) to the experimentally recorded (solid circles) Raman response of a MAPbI1.5Br1.5 thin film.Fits reflect the sum over three phonon modes, together with a small quasi-elastic (QE) scattering response.

Figure S7 .
Figure S7.Damped harmonic oscillator model fits (solid lines) to the experimentally recorded (solid circles) Raman response of a MAPbBr3 thin film.Fits reflect the sum over three phonon modes, together with a small quasi-elastic (QE) scattering response.

Figure S8 .
Figure S8.Damped harmonic oscillator model fits (solid lines) to the experimentally recorded (solid circles) Raman response of a CsPbBr3 thin film.Fits reflect the sum over three phonon modes, together with a small quasi-elastic (QE) scattering response.

Figure S9 .
Figure S9.Damped harmonic oscillator model fits (solid lines) to the experimentally recorded (solid circles) Raman response of a FAPbI3 thin film.Fits reflect the sum over three phonon modes, together with a small quasi-elastic (QE) scattering response.

Figure S10 .
Figure S10.Damped harmonic oscillator model fits (solid lines) to the experimentally recorded (solid circles) Raman response of a PbI2 thin film.Fits reflect the sum over three phonon modes.

Figure S11 .
Figure S11.Damped harmonic oscillator model fits (solid lines) to the experimentally recorded (solid circles) Raman response of a Cu2AgBiI6 thin film.Fits reflect the sum over four phonon modes, together with a small quasi-elastic (QE) scattering response.

Figure S12 .
Figure S12.Damped harmonic oscillator model fits (solid lines) to the experimentally recorded (solid circles) Raman response of a Cs2AgBiBr6 thin film.Fits reflect the sum over four phonon modes, together with a small quasi-elastic (QE) scattering response.

Figure S13 .
Figure S13.Damped harmonic oscillator model fits (solid lines) to the experimentally recorded (solid circles) Raman response of a AgI thin film.Fits reflect the sum over three phonon modes, together with a small quasi-elastic (QE) scattering response.

Figure S14 .
Figure S14.Damped harmonic oscillator model fits (solid lines) to the experimentally recorded (solid circles) IR response in the THz region for a MAPbI3 thin film.Fits reflect the sum over two phonon modes.

Figure S15 .
Figure S15.Damped harmonic oscillator model fits (solid lines) to the experimentally recorded (solid circles) IR response in the THz region for a MAPbI1.5Br1.5 thin film.Fits reflect the sum over two phonon modes.

Figure S16 .
Figure S16.Damped harmonic oscillator model fits (solid lines) to the experimentally recorded (solid circles) IR response in the THz region for a MAPbBr3 thin film.Fits reflect the sum over two phonon modes.

Figure S17 .
Figure S17.Damped harmonic oscillator model fits (solid lines) to the experimentally recorded (solid circles) IR response in the THz region for a CsPbBr3 thin film.Fits reflect the sum over two phonon modes.

Figure S18 .
Figure S18.Damped harmonic oscillator model fits (solid lines) to the experimentally recorded (solid circles) IR response in the THz region for a FAPbI3 thin film.Fits reflect the sum over two phonon modes.

Figure S19 .
Figure S19.Damped harmonic oscillator model fits (solid lines) to the experimentally recorded (solid circles) IR response in the THz region for a PbI2 thin film.Fits reflect the sum over two phonon modes.

Figure S20 .
Figure S20.Mode frequencies extracted from fits of the damped harmonic oscillator model to the Raman spectra of MAPbI3, MAPbI1.5Br1.5 and MAPbBr3 thin films.

Figure S21 .
Figure S21.Mode frequencies extracted from fits of the damped harmonic oscillator model to the IR spectra of MAPbI3, MAPbI1.5Br1.5 and MAPbBr3 thin films.

Table 1 .
Oscillator mode frequencies and broadening extracted from fitting damped harmonic oscillator response to Raman and IR spectra in the THz region for various thin films.Fitting details can be found earlier in Section 4.